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A248705 The cubes related to the strictly increasing subsequence of A053668(n), n >= 1. 1
1, 8, 27, 64, 343, 729, 2744, 3375, 6859, 35937, 46656, 148877, 287496, 438976, 778688, 2985984, 3869893, 8489664, 34645976, 43986977, 58863869, 75686967, 398688256, 426957777, 485587656, 596947688, 835896888, 1693669888, 2548895896, 2954987875, 4758586568 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The triangular numbers of this form are at A246753.
The squares of this form are at A248648.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..139 (first 116 terms from K. D. Bajpai)
EXAMPLE
a(4) = 64 = 4*4*4, which is a cube. Product of its digits = 6*4 = 24.
a(5) = 343 = 7*7*7, which is a cube. Product of its digits = 3*4*3 = 36.
Since 36 > 24, 64 and 343 appear in the sequence.
As suggested by Wolfdieter Lang, examples further clarified:
(Start)
A053668 is sieved (from left to right):
1, 2, 3, 4, 5, 6, 7, 8, 9, ....(numbers: k)
1, 8, 27, 64, 125, 216, 343, 512, 729, ....(cubes: k^3)
1, 8, 14, 24, 10, 12, 36, 10, 126, ....(prod of digits of k^3)
1, 8, 14, 24, X, X, 36, X, 126, ....(sieved products)
and related leftover cubes are:
1, 8, 27, 64, 343, 729, ....(leftover cubes)
(End)
MATHEMATICA
A248705 = {}; t = 0; Do[s = Apply[Times, IntegerDigits[n^3]]; If[s > t, t = s; AppendTo[A248705, n^3]], {n, 1, 10^4}]; A248705
PROG
(PARI) \\ For b-file
c = 0; k = 0; for(n=1, 5*10^8, d = digits(n^3); p = prod(i = 1, #d, d[i]); while(p > k, c++; print(c, " ", n^3); k = p))
(Python)
from operator import mul
from functools import reduce
A248705_list, x, m = [], 0, [6, -6, 1, 0]
for _ in range(10**9):
for i in range(3):
m[i+1]+= m[i]
xn = reduce(mul, [int(d) for d in str(m[-1])], 1)
if xn > x:
x = xn
A248705_list.append(m[-1]) # Chai Wah Wu, Nov 19 2014
CROSSREFS
Sequence in context: A121652 A112989 A018832 * A030293 A030479 A061096
KEYWORD
nonn,base
AUTHOR
K. D. Bajpai, Oct 13 2014
STATUS
approved

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Last modified June 20 14:54 EDT 2024. Contains 373526 sequences. (Running on oeis4.)